We report a search for the lepton-flavor-violating decays $\tau^{ \pm}\to\ell^{ \pm}\alpha$~($\ell=e,\mu$), where $\alpha$ is an undetected spin-0 particle, such as an axion-like particle using $736\times10^{ 6}$ tau lepton pairs collected by the Belle detector at the KEKB asymmetric-energy $e^{ +}e^{ -}$ collider. We find no evidence of signal and obtain the most stringent upper limits on the branching fractions at 95\% confidence level: $\mathcal{ B}(\tau^{ \pm}\rightarrow e^{ \pm}\alpha)$ $<$ $(0.4$--$6.4)\times10^{ -4}$ and $\mathcal{ B}(\tau^{ \pm}\rightarrow \mu^{ \pm}\alpha)$ $<$ $(0.2$--$3.5)\times10^{ -4}$ at 95\% confidence level for an $\alpha$ mass in the range $0.0\leq m_{ \alpha}\leq 1.6$~GeV/$c^{ 2}$.
Categories: hep-ex